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"...Chess has been finely honed by natural selection to be free of arbitrariness. Every rule and piece in Chess serves a purpose, and none are arbitrary. Since Chess is what won the survival of the fittest among Chess variants, I expect that any variant capable of succeeding Chess would also have to be free of arbitrariness. But most Chess variants differ from Chess through some arbitrary change to it, and they easily get lost in a sea of variants that each differ from Chess in their own arbitrary ways..."

I'll try to show that chess is free of arbitrariness. Let's say Ks are needed for the thrill of the chase, so each side can hope to checkmate. A board of some size & shape (& each side's army) must be chosen. There's to be infantry (say Ps) that can promote, if only to avoid a high % of draws happening because lots of better pcs are traded (capturing enemy pcs or Ps being logical), besides initially providing a buffer between the pcs of each army.

We can see that a 5x2 rect board is too small no matter what pc is with each K, and 6x2 isn't better. A 6x3 board creates more possibilities for pcs, but a rect board is unattractive for many people's tastes, so try a sq 6x6 board (other shapes tried later). In that case a variant becomes viable, except games might be shorter than desirable, & a logical pc type to have, a B, is liable to be less of a match for another logical pc type (the N, as will be explained). That's since we know from hindsight that on an 8x8 sq board, a N is an almost perfect match for a B, in terms of value, on average.

Why is a N a logical pc type to have? Unlike the B, it moves to a sq on the opposite colour to which it starts, and it does so in a convoluted but logical way: it can leap to any of the second closest such coloured sqs to it. If a N moved to the nearest opposite coloured sqs to it, it would always be able to move to too few sqs, & it would be moving like a weak version of a R, which is another logical pc type to have for a sq board. Since there should be 2 opposite coloured Bs per side on a sq board, it's logical to have two Ns & two Rs also. Plus a K, that's 7 pcs per side on our 8x8 sq board size. So, what should the final pc be in each side's army?

A K ought to have a wife (Q), & it's nice that there's only going to be one per side, at least to start with (with Ps that can promote, it's possible that a K may become a bigamist later in the game). It would be good if a Q moves the same way as a K, except most games would be long as a result, & exciting early middlegame or opening attacks aren't feasible. This perhaps led to the thought of the Q movement rules of modern chess, where a Q moves like a R&B. This particular combination of powers means that a Q is often very effective at checkmating a K, with very little assistance at times. If a Q moved like N&B (or N&R) instead of R&B, it would be less effective at checkmating attacks, for example. In hindsight, this reinforces the basic way we decide to move a K, i.e. as a now weaker version of a Q.

One might ask, why not have the Q move like a N besides moving like a R&B? Well, such a pc is too powerful to be desirable in many chess variants, especially on a board only 8x8. Such a pc is also capable of mating with absolutely no assistance at times. Another reason not to use such a pc comes from an additional reason that the N is a logical pc type to include: undefended, it can fearlessly attack a Q (or any other pc type we've included), since a Q cannot move the same way.

The Ps, to be logical pc types that are the backbone of an army, should advance cautiously forward one sq at a time, &, to punish premature commitment, never retreat (the initial double step option is allowed to speed up the opening phase of the game [leading to the en passant capture rule, too], but, e.g., a triple step on an 8x8 sq board would be undesirable, as that would put a P in the opponent's half of the board immediately, & bring the chance of promotion arguably too soon). The Ps can change files due to their diagonal capturing rule, which may serve to open files for major pcs.

Having decided on the composition of each side's army for an 8x8 sq board, how to arrange the starting position for the armies? It's logical to have all the Ps on each side's 2nd rank, if only to create the nice possibilites of back rank or smothered checkmates. How to arrange the 8 pcs behind them? Fischer Random (aka Chess960) allows for many ways to do this, but I'll try to argue chess has the best starting position given the existing pcs. First of all, the royal pcs logically belong on the central files' 2 squares, and the Bs are evidently on the two best sqs for their future development possibilities, based on experience.

The Ns, where they are to start from, often develop to KB3 or even QB3, which are sqs that nicely affect the battle for the centre being fought by Ps (sooner or later), or perhaps help defend the K; in any case the minor pcs are placed symmetrically, which is desirable. To connect the Rs or improve K safety, the possiblity of castling to either side is allowed, K moving 1st & double stepping, K- & Q-side castling positions nearly sym w/o K or R trading sq. The hardest thing to say that's not arbitrary is the starting positions for the royal pcs, & which colour the right hand sq on one's first rank should be. It's desirable that royalty be placed in the mirror image of the enemy army's royalty, but whether to have White's Q on the left of the K, or on the right?

To avoid saying it's simply due to convention, I'd guess the old saying 'one's right hand man' goes against having the Q to the right of White's K, & common O-O is right-handedly physically easier too (Black's Q will be right of his K, but that's just one more 'indignity' of having the Black pcs, I'd further speculate). Similarly, having h1 as a light sq means one can now recall the saying 'The Q goes on her own colour' when setting up the pcs, which somehow sounds nicer (mentioning a lady) than 'The K goes on his own colour', if h1 were a dark sq.

Let's return to the question of the terrain, & ask why a board that's a different shape might not be just as nice, too. In Circular Chess there's 64 cells (rather than sqs), i.e. 4 rings ('ranks') of 16 'files'. The pc types used for chess are best. In this variant Rs are much stronger than minor pcs, yet K&R are normally unable to mate, & neither of these features is particularly desirable. There are some compensating features for this, in that K&P always wins vs. K (stalemate being impossible), & the novel terrain makes the game more challenging in a way than chess. Yet there seems less variety for the opening phase, & Exchange sacrifices or R for 2 pc trades are seldom interesting, so the game also seems poorer than chess these ways too, at least to my untrained eyes.

In Hexagonal Chess, 91 hex-shaped cells (of 3 colours) are used to make a hex shaped board. The pc types used for chess are best. Here Ns are actually stronger than Bs (by a P), though interesting trades of N for B&P may be not uncommon, especially as there are 3 Bs. Still, Ns here have less roles than in chess, as a position can never become truly closed, and at least one diagonal pc can always 'see' into the enemy camp, if moved to a suitable hex. N outposts also seem less of a concept in this game. Like for Circular Chess, the terrain of this game provides some compensating features that make up a little for what the game lacks compared to chess.

Getting back to chess, in hindsight we can say that the many different roles of the non-arbitrary pc types seem to have allowed for a rich number of chess openings & situations in the other phases of the game. It will still be a long time before chess opening theory has been pretty much exhausted, as far as the most promising openings go. One thing I have yet to mention is draws in chess, which are more frequent in high level games (perhaps such players should play on in dull positions more often, if they arise). What about stalemate being a draw? It's logical that a player who has an advantage is sometimes punished for flawed technique if stalemate is ruled to be a draw, rather than a win for one side (or, say, 3/4 of a point). Good defence is also not punished if a stalemate is a draw, and some very fine stalemate combinations/swindles happen from time to time (& many endgames would otherwise be lost for one side, too). 50 move rule/draw by 3-fold repetition/perpetual is logical (50 is a nice, high, round number); in the case of a repetition, 1st can be test of intent.

Another thing that might have been used in chess is 'drops' onto the board of previously captured enemy pcs, as in Crazyhouse, Bughouse and Japanese Chess (aka Shogi). While such drops of pcs may make the game more tactical & exciting, these games are less strategic (or logical, at least in Western eyes) than many games of chess can be, & the average length of such games may not be the nice average of 40 moves that chess has for a game.

To sum up, I'd agree with Fergus' opinion (as quoted at the beginning of this blog entry). Indeed, I find it hard to imagine a more logical board game of skill than chess. Perhaps others sense this too, & that's one of the reasons why chess is so popular (the visual attractiveness of a chess set doesn't hurt either). I also agree with Fergus in that I think many other chess variants certainly have merits, i.e. some of their features compensate to some extent for what they may lack when compared to, say, chess. Shogi and Chinese Chess are classics too; the former has 10 million that play in Japan, the latter 200 million playing globally ('Go' has 40 million), while 600 million adults play chess.